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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">s2</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>





<b>set </b><font color="Maroon">Cs1</font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font>;<br/>
<b>set </b><font color="Maroon">Cs2</font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font>;<br/>
<b>set </b><font color="Maroon">D</font> = <span class="p1">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:23"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s1</font> &amp; <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s2</font> &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> (  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">j</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> &amp;  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">j</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> ) ) &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span> )
 ;<br/>

<b>reconsider </b><font color="Maroon">t</font> =  <a href="xboole_0.html#K1">{}</a>  as    <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmfsa_2.html#K1">SCM+FSA</a>  <b>by </b><i><a class="ref" href="ami_1.html#T63">AMI_1:63</a></i>;<br/>
<b>set </b><font color="Maroon">D1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>;<br/>
<a NAME="E3:23"/><i><font color="Green">E42</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font> <a href="tarski.html#R1">c=</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="finsub_1.html#K1">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T60">RELAT_1:60</a>, <a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E4:23"/><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">t</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>;<br/>
<b>hence </b><a NAME="E5:23"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
 <b>by </b><i>, , </i>;<br/>

<b>thus </b><a NAME="E6:23"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s1</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s2</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 <b>by </b><i>, , , </i>;<br/>


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